A244398 - OEIS

%I #13 Feb 09 2015 10:48:26

%S 1,2,5,10,22,45,97,206,450,982,2178,4849,10904,24630,56010,127911,

%T 293546,676156,1563371,3626148,8436378,19680276,46026617,107890608,

%U 253450710,596572386,1406818758,3323236237,7862958390,18632325318,44214569099,105061603968

%N Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 2.

%H Alois P. Heinz, <a href="/A244398/b244398.txt">Table of n, a(n) for n = 3..1000</a>

%F a(n) = A001190(n+1)-1 = A036656(n+1)-1.

%F a(n) ~ c * d^n / n^(3/2), where d = 2.4832535361726368... = A086317 and c = 0.7916031835775118... = A086318. - _Vaclav Kotesovec_, Jun 27 2014

%p b:= proc(n, i, t, k) option remember; `if`(n=0, 1,

%p       `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*

%p        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))

%p     end:

%p a:= n-> b(n-1$2, 2$2) -`if`(n=0, 0, 1):

%p seq(a(n), n=3..40);

%t b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[b[i-1, i-1, k, k]+j-1, j]*b[n-i*j, i-1, t-j, k], {j, 0, Min[t, n/i]}]] // FullSimplify]; a[n_] := b[n-1, n-1, 2, 2] - If[n == 0, 0, 1]; Table[a[n], {n, 3, 40}] (* _Jean-François Alcover_, Feb 09 2015, after Maple *)

%Y Column k=2 of A244372.

%Y Cf. A001190, A036656, A086317, A086318.

%K nonn

%O 3,2

%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014